Question

A fair coin is tossed $8$ times. Find the probability that it shows heads at least once.

Answer 1

$p=$ probability of a head on a fair coin
$p=\frac{1}{2},q=1-\frac{1}{2}=\frac{1}{2}$
If head don't come any time
Probability $={{}^{8}C}_0{p}^0{q}^8={{}^{8}C}_0{\left(\frac{1}{2}\right)}^0{\left(\frac{1}{2}\right)}^8$
$=1\times \frac{1}{2^8}=\frac{1}{256}$
$\therefore$ shows heads atleast once$=1-\frac{1}{256}=\frac{255}{256}$